Dartmouth College - Department of Mathematics; Dartmouth College - Department of Computer Science

Date Written: April 30, 2016

Abstract

Legal reasoning requires identification, through search, of authoritative legal texts (such as statutes, constitutions, or prior judicial decisions) that apply to a given legal question. In this paper we model the concept of the law search as an organizing principle in the evolution of the corpus of legal texts, apply that model to U.S. Supreme Court opinions. We examine the underlying navigable geometric and topological structure of the Supreme Court opinion corpus (the "opinion landscape") and quantify and study its dynamic evolution. We realize the legal document corpus as a geometric network in which nodes are legal texts connected in a weighted and interleaved fashion according to both semantic similarity and citation connection. This network representation derives from a stylized generative process that models human-executed search via a probabilistic agent that navigates between cases according to these legally relevant features. The network model and (parametrized) probabilistic search behavior give rise to a PageRank-style ranking of the texts -- already implemented in a pilot version on a publicly accessible website -- that can be compared to search results produced by human researchers. The search model also gives rise to a natural geometry through which we can measure change in the network. This enables us to then measure the ways in which new judicial decisions affect the topography of the network and its future evolution. While we deploy it here on the U.S. Supreme Court opinion corpus, there are obvious extensions to larger bodies of evolving bodies of legal text (or text corpora in general). The model is a proxy for the way in which new opinions influence the search behavior of litigants and judges and thus affect the law. This type of legal search effect is a new legal consequence of research practice that has not been previously identified in jurisprudential thought and has never before been subject to empirical analysis. We quantitatively estimate the extent of this effect and find significant relationships between search-related network structures and propensity of future citation. This finding indicates that influence on search is a pathway through which judicial decisions can affect future legal development.

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